Question: $A$ $B$ $C$ If: $ AB = 4x + 6$, $ BC = 3x + 7$, and $ AC = 62$, Find $BC$.
Answer: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {4x + 6} + {3x + 7} = {62}$ Combine like terms: $ 7x + 13 = {62}$ Subtract $13$ from both sides: $ 7x = 49$ Divide both sides by $7$ to find $x$ $ x = 7$ Substitute $7$ for $x$ in the expression that was given for $BC$ $ BC = 3({7}) + 7$ Simplify: $ {BC = 21 + 7}$ Simplify to find ${BC}$ : $ {BC = 28}$